Device and method for training a normalizing flow

Abstract

A computer-implemented method for training a normalizing flow. The normalizing flow predicts a first density value based on a first input image. The first density value characterizes a likelihood of the first input image to occur. The first density value is predicted based on an intermediate output of a first convolutional layer of the normalizing flow. The intermediate output is determined based on a plurality of weights of the first convolutional layer. The method for training includes: determining a second input image; determining an output, wherein the output is determined by providing the second input image to the normalizing flow and providing an output of the normalizing flow as output; determining a second density value based on the output tensor and on the plurality of weights; determining a natural gradient of the plurality of weights with respect to the second density value; adapting the weights according to the natural gradient.

Description

CROSS REFERENCE[0001]The present application claims the benefit under 35 U.S.C. 119 of European Patent Application No. EP 20194550.8 filed on Sep. 4, 2020, which is expressly incorporated herein by reference in its entirety.FIELD[0002]The present invention concerns a method for training a normalizing flow, a method for using a normalizing flow, a method for classifying images by means of a normalizing flow, a normalizing flow, an image classifier, a computer program and a machine-readable storage medium.BACKGROUND INFORMATION[0003]L. Gresele, G. Fissore, A. Javaloy, B. Schölkopf, A. Hyvärinen, “Relative gradient optimization of the Jacobian term in unsupervised deep learning,” Jun. 26, 2020, https: / / arxiv.org / abs / 2006.15090v1 describes a method for training a fully connected normalizing flow.SUMMARY[0004]Determining the probability of an image to occur is a central problem in many technical applications. The probability of an image to occur may be understood as a probability for rec...

AI Technical Summary

Benefits of technology

The patent text explains the importance of choosing the right model for a device that predicts the initial density of an environment. Using one of the described image classifiers can help the device make more accurate predictions and operate in a safer, reliable, and expected manner. The technical effect of this is that the device can better understand its surroundings and make informed decisions.

Problems solved by technology

Determining the probability of an image to occur is a central problem in many technical applications.

One of the fundamental limitations of such models is the restriction that the determinant of the Jacobian of the transformation achieved by the deep convolutional neural network must be easily computable to allow for efficient training through maximization of the likelihood of the data.

However, these constrained function classes ultimately result in suboptimal models of the probability density of the image data due to their fundamental limited representational power.

However, finding such a model is complicated due to the high-dimensionality of the probability distribution.

Unfortunately, computing the gradient for the first convolutional layer of the normalizing flow this way generally requires an inversion of a matrix, wherein the computational complexity of the inversion is cubical in the number of weights of the first convolutional layer.

However, these special layers restrict the transformations that can be achieved by a normalizing flow and hence negatively influence the accuracy of the mapping of the normalizing flow.

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